A. Energy Dissipation as a Limiting Factor in Logic Design
There is a body of literature on reversible computation [11] which shows that the energy dissipation per device operation (e.g., per gate operation in a computational context) cannot be reduced below In(2) kT (where k is Boltzman's constant and T is the temperature, such that kT is an approximation of the thermal energy of a single atom) if the device is not reversible.
For the last few decades the energy dissipation per gate operation has been declining with remarkable regularity [6]. Extrapolation of this trend indicates the energy dissipation per device operation might reach kT in the next couple of decades or so (assuming T is 300 Kelvins). To provide some perspective on the challenge involved in attaining that result, it may be helpful to note that an "AND" gate which has a power supply of one volt and which allows a single electron to go from that one volt supply to ground during the course of a switching operation will dissipate one electron volt. Although one electron volt is about forty times kT (and well above the theoretical limit), it clearly will be difficult for simple improvements in irreversible logic to reach an energy dissipation level as low as even one electron volt.
Furthermore, even if the energy dissipation per gate operation could be reduced to In(2) kT, a computer operating at room temperature at a frequency of 1 GHz with 10.sup.18 logic gates packed into a cubic centimeter would dissipate roughly three megawatts. Thus, it is reasonable to assume that the desire for ever greater computational power with ever more densely packed logic elements will eventually require that a single logic operation dissipate at least several orders of magnitude energy less than kT.
Heretofore, refrigeration has been employed in some computers for removing the heat they generate during operation. Refrigeration reduces the energy dissipation per gate operation, but it does not reduce the overall energy dissipation. At best, the lower energy required per gate operation is almost exactly balanced by the increased energy needed for the refrigeration.
Of course, factors other than net energy savings can make low temperature operation worthwhile in certain situations. For example, some potentially attractive devices require a refrigerated environment for proper operation. Thus, in large computers operating in stable environments (the traditional computer center, for example) refrigeration might be attractive, particularly if it permits the use of devices, such as Josephson junction devices, that provide much better performance but which require low temperature for their operation. However, even if net energy savings need not be considered, refrigeration per se is not an attractive, general purpose technique for reducing the energy dissipation per gate operation because lap top and portable computers [59], embedded systems, various "smart" appliances and other applications commonly operate in non-refrigerated environments.